468
zinc metallurgical recovery in lead concentrate. The same behavior is observed in the test
set, where 3 out of the 10 samples showed sum above one. Furthermore, it was identified
two negative values for zinc metallurgical recovery in tailings and one prediction above one
for zinc metallurgical recovery in zinc concentrate. These results show the need to do a post
processing before using them in practice.
2.3 Artificial neural networks
2.3.1 Background theory
The mathematical representation of a neural network with one hidden layer, such as the one
used in this study, is presented below starting with the equations representing the input and
hidden layer connections:
j
i
d
ji i
=
∑
0
β j
∑ ∑
(12)
z j
j
ϕ ( )
v j
v
ϕ
(13)
Figure 3. Observed values against predicted thru the use of the models built.
Table 2. Observed against predicted correlations using regression models.
Variable
Training set
Test set
Zn Conc. Mass Recovery
0.993
0.989
Pb Conc. Mass Recovery
0.621
0.442
Tailings Mass Recovery
0.992
0.989
Zn Met. Recovery in Zn Conc.
0.951
0.928
Zn Met. Recovery in Tailings
0.937
0.913
"0
."l
0.6
~ 0.4
£ 0.2
Zn Cone. Mass Recovery
0.0 ¥"....._~-~-~~-~-~---1
0.0 0.1 0.2 0.3 0.4 0.5 0 .6 0. 7
Observed
0. 3 0.4 0 .5
0.6 0.7
0.8 0 .9
1.0
Observed
Pb Cone. Mass Recovery
0 .020 . . -------'---'---'---'--'-----71
0 .015
*
:6 0 .010
.; . *
£
0 .005
0.005
0 .010
Observed
0 .015
0.020
Zn Met. Recovery in Zn Cone.
1.0
a: 0.8
~
ct 0.6
0.4
0.4
0.6
0.8
1.0
Observed
o. 8 . ,_ z _n _ M _e _t_. _ R_ e_ co _v_e _r_oy_i_n_ T _a _i_ l in _g =-s -~
0.6
il
~ 0.4
~
a.. 0.2
0.0
0 .2
0.4
Observed
e Test
* Train ing
*
0 .6
0.8